Question: Calculate the maximum absorption rate from oxygen in air bubbles with a pressure of 1 atm and a diameter of 100 m in a fermenter

Calculate the maximum absorption rate from oxygen in air bubbles with a pressure of 1 atm and a diameter of 100 m in a fermenter to water at 37oC. Initially, the amount of dissolved oxygen in water is 0. The solubility of oxygen in air in water is 2.26x10-7 gmol O2 / cm3 liquid at 37oC. The diffusivity of oxygen in water is 3.25x10-9 m2 / s at 37oC. You can consider the mass transfer resistance from the inside face to the outside of the bubble to be negligible.

kL = 2D US + 0,31Sc-2 / 3cgc21 / 3 kL: mass transfer coefficient (m2 / s) D: diameter of gas bubble (m) c: viscosity of the solution (Pa.s) g: gravitational acceleration Sc: Schmidt number c: density of the continuous phase p: density of the gas bubble, 1.13 kg / m3 = c - p, > 0

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